Minimal mesoscale model for protein-mediated vesiculation in clathrin-dependent endocytosis

Abstract

In eukaryotic cells, the internalization of extracellular cargo via the endocytic machinery is an important regulatory process required for many essential cellular functions. The role of cooperative protein-protein and protein-membrane interactions in the ubiquitous endocytic pathway in mammalian cells, namely the clathrin-dependent endocytosis, remains unresolved. We employ the Helfrich membrane Hamiltonian together with surface evolution methodology to address how the shapes and energetics of vesicular-bud formation in a planar membrane are stabilized by presence of the clathrin-coat assembly. Our results identify a unique dual role for the tubulating protein epsin: multiple epsins localized spatially and orientationally collectively play the role of a curvature inducing capsid; in addition, epsin serves the role of an adapter in binding the clathrin coat to the membrane. Our results also suggest an important role for the clathrin lattice, namely in the spatial- and orientational-templating of epsins. We suggest that there exists a critical size of the coat above which a vesicular bud with a constricted neck resembling a mature vesicle is stabilized. Based on the observed strong dependence of the vesicle diameter on the bending rigidity, we suggest that the variability in bending stiffness due to variations in membrane composition with cell type can explain the experimentally observed variability on the size of clathrin-coated vesicles, which typically range 50-100 nm. Our model also provides estimates for the number of epsins involved in stabilizing a coated vesicle, and without any direct fitting reproduces the experimentally observed shapes of vesicular intermediates as well as their probability distributions quantitatively, in wildtype as well as CLAP IgG injected neuronal cell experiments. We have presented a minimal mesoscale model which quantitatively explains several experimental observations on the process of vesicle nucleation induced by the clathrin-coated assembly prior to vesicle scission in clathrin dependent endocytosis.

Figure 1. Reaction scheme for the clathrin coated vesicle formation.

The free energy of state 2 relative to state 1 is described by E_t.

Figure 2. A schematic of the membrane profile explaining the variables in the surface evolution methodology.

The full membrane profile is obtained by rotating the curve by 2π about the z-axis.

Figure 3. Membrane deformation profiles under curvature fields.

(a) Three different membrane deformation profiles under the influence of imposed curvature of the epsin shell model for three different coat areas; here κ = 20 k_BT. For the largest coat area, the membrane shape is reminiscent of a clathrin-coated vesicle. (b) Vesicle neck-radius as a function of coat area A_a.

Figure 4. Membrane deformation profiles for mature vesicular buds under the influence of imposed curvature of the epsin shell model for different values of the membrane bending rigidity.

Figure 5. Distribution of vesicular intermediates.

(a) Calculated and (b) experimental probability of observing a clathrin-coated vesicular bud of given size in WT cells (filled) and CLAP IgG injected cells (unfilled). In the calculated histogram, the four categories defined are based on the progression of bud growth. Category 2 includes all buds for which bud diameter is less compared to the neck radius, while category 4 includes all buds for which bud diameter is more compared to the neck radius. Category 3 is an intermediate case between category 2 and 4.